Question

Suppose a company has fixed costs of $47,600 and variable cost per unit of

4/9x+ 333 dollars,

where x is the total number of units produced. Suppose further that the selling price of its product is

1767 −5/9x

x dollars per unit.

(a) Find the break-even points. (Enter your answers as a comma-separated list.)
x =  

  

(b) Find the maximum revenue. (Round your answer to the nearest cent.)
$  

(c) Form the profit function P(x) from the cost and revenue functions.
P(x) =  

  

Find maximum profit.
$  

(d) What price will maximize the profit? (Round your answer to the nearest cent.)
$

Answer 1

Fixed cost = $47,600

Variable cost per unit is :

So variable cost of x unit is :

So total costs of unit = variable cost of x unit + fixed cost

Selling price per unit =

So we can say revenue per unit is =

So revenue of x unit is

So Profit = Revenue - Total cost

  

  

So break even point when profit = 0

So we can write:

So

  

So or   

or

So break even point at x = 34 or x = 1400

(b) As we find revenue function is:

For finding maximum revenue we find derivative of revenue

We can make it equal to zero for maximum revenue

Second derivative of revenue function is:

So at x = 1590.3 we will get maximum revenue.

So maximum revenue is :

We get profit function as:

For maximum profit

Second derivative of profit function is:

P''(x) = -2

So we will get maximum profit at x = 717